THE CONNECTIVITY OF MAXIMUM MATCHING GRAPHS

The maximum matching graph of a graph has a vertex for each maximummatching and an edge for each pair of maximum matchings which differ by exactly oneedge. In this paper, we prove that the connectivity of maximum matching graph of abipartite graph is equal to its minimum degree.     

THE RATE OF UNIFORM CONVERGENCE OF THE SURVIVAL FUNCTION ESTIMATOR FOR TRUNCATED AND CENSORED DATA

1 Illtroduction and Main ResultsIn medical follow-up or engineering life testing studies one may not be able to observethe variable of inferest, referred to hereafter as the lifetime. Among the differellt forms inwhich incomplete data appears right censoring and left truncation are two common ones. Lefttruncation mad occur if the time origin of the lifetime precedes the time origin of the study.Only subjects that fail after the start of the study are being followed, otherwise they are lefttru…     

关于平稳序列的自相关矩阵的正定性

平稳序列的自相关矩阵R(n)是非负定的。利用斯梯阶积分和纯跳跃函数的性质,本文通过积分谱F(ω)表达了R(n)为正定的充分必要条件,并得到了平稳过程的对偶结论。     

ASYMPTOTIC BEHAVIOR OF THE ESTIMATES OF HIGHER ORDER SPECTRA UNDER TRUNCATED WINDOW

ＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＴＨＥＥＳＴＩＭＡＴＥＳＯＦＨＩＧＨＥＲＯＲＤＥＲＳＰＥＣＴＲＡＵＮＤＥＲＴＲＵＮＣＡＴＥＤＷＩＮＤＯＷＹＵＤａｎ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎ...     

ON CONVERGENCE AND RATE OF CONVERGENCE OF ALGORITHMS IN THE MOVER－STAYER MODEL

ＯＮＣＯＮＶＥＲＧＥＮＣＥＡＮＤＲＡＴＥＯＦＣＯＮＶＥＲＧＥＮＣＥＯＦＡＬＧＯＲＩＴＨＭＳＩＮＴＨＥＭＯＶＥＲ－ＳＴＡＹＥＲＭＯＤＥＬＷＡＮＧＤｏｎｇｑｉａｎ；Ｌａｗｏｋｏ，Ｃ．Ｒ．Ｏ．（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，ＭａｓｓｅｙＵｎ...     

MAXIMUM PRINCIPLE FOR THE OPTIMAL CONTROL OF AN ABLATION-TRANSPIRATION COOLING SYSTEM

This paper is concerned with an optimal control problem of an ablationtranspiration cooling control system with Stefan-Signorini boundary condition. The existence of weak solution of the system is considered. The Dubovitskii and Milyutin approach is adopted in the investigation of the Pontryagin‘s maximum principle of the system. The optimality necessary condition is presented for the problem with fixed final horizon and phase constraints.     

AN INVESTIGATION OF THE POLYNOMIAL FORFORWARD ANALYSIS OF A FLORIDA PLATFORM

1.IntroductionInthisreportwewillpresentsomecomputationalresultsforthekinematicsolutionofanin-parallelmechanismplatformdesignedattheUniversityofFlorida.Thefigureoftheplatformanalysedhereisasfollows.Figure1Theconnectingpointsjoinvenicestosidesofthepairoftriangles.Thisisaspecialcaseofwhatwehaveconsideredin[l].Sincebothofthefixedandmovingplatformsaretriangles,andsomejointcenterslieonthecorrespondingsidesofthem,wecanspecifysomeparametersin[1]foranalysis.Itturnsoutthatmorecomputationalresultscanbe…     

MULTIPLICITY-PRESERVING TRIANGULAR SET DECOMPOSITION OF TWO POLYNOMIALS

In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence of two polynomials once and certain GCD computations. The algorithm decomposes the unmixed variety defined by two polynomials into square free and disjoint （for non-vertical components, see Definition 4） algebraic cycles represented by triangular sets which may have negative multiplicities. Thus, the authors can count the multiplicities of the non-vertical components. In the bivariate case, the amthors give a complete algorithm to decompose tile system into zeros represented by triangular sets with multiplicities. The authors also analyze the complexity of the algorithm in the bivariate ease. The authors implement the algorithm and show the effectiveness of the method with extensive experiments.     

CONVERGENCE PROPERTIES OF MULTI-DIMENSIONAL NEAREST NEIGHBOR DENSITY ESTIMATES FOR THE CASE OF GENERAL KERNEL

In this paper we give weaker conditions to ensure the strong uniform consis-tency of multi-dimensional nearest neighbor (N.N.) estimates with non-uniform kernel andobtain the convergence rates of these estimates on an arbitrary bounded set. The ratescan not be improved in some sense. Obviously, the problem of strong convergence rates ata given point is its special case. The range of applications of estimates is extended.     

ON THE BEST UNIFORM CONVERGENCE RATE OF EB ESTIMATORS

ＯＮＴＨＥＢＥＳＴＵＮＩＦＯＲＭＣＯＮＶＥＲＧＥＮＣＥＲＡＴＥＯＦＥＢＥＳＴＩＭＡＴＯＲＳＬＩＡＮＧＨｕａ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）ＹＵＡＮＹａｈｕａ（...     

THE CONVERGENCE OF BROYDEN ALGORITHMSWITHOUT CONVEXITY ASSUMPTION

1.IatroductionWeknowthatthevariablemetricalgorithms,suchastheBroydenalgorithms[1],areveryusefulandefficientmethodsforsolvingthenonlinearprogrammingproblem:min{f(x);xERn}.(1.1)Withexactlinesearch,Powelll2]provedthattherateofconvergenceofthesealgorithmsisone-stepsuperlinearfortheuniformlyconvexobjectivefunction,andifthepoiedsgivenbythesealgorithmsareconvergeal,PnandYul3]provedthattheyaregloballyconvergelitforthecolltinuousdifferentiablefunction.Withoutexactlinesearchseveralresultshavebeenobtai…     

FIXED POINTS OF THE lTH POWER OF DIFFERENTIAL POLYNOMIALS GENERATED BY SOLUTIONS OF DIFFERENTIAL EQUATIONS

In this paper, we study the problem on the fixed points of the lth power of linear differential polynomials generated by second order linear differential equations. Because of the control of differential equation, we can obtain some precise estimate of their fixed points.     

A MODEL FOR THE“MAXIMUM CAPACITY” OF ROOMS OR OF SPACE

A discrete optimum mathematical model to derive the "maximum capacity" of people in a roomor in a space used for public gatherings is developed. There are two outcomes in the model. One isfocused on whether the person farthest from exits can escape from the room. The other concentrateson the evacuation time of all the people in the room. According to the results of the two outcomes, amore reasonable "maximum capacity" can be worked out in a simple way.     

UMVUE OF POLYNOMIALS OF (EX)~(-1) FOR SEVERAL NATURAL EXPONENTIAL FAMILIES ON THE POSITIVE LINE

1. IntroductionBecause of its applications ill biological science and econometrics as well as in experimental nuclear physics, some authors[1'2] have studied the unbiased estimation of the inverse ofpopulation mean! 1/m. Srivatava and Bhatnagar used the statisticXti '~ ~ k > 0, (1.1)X. k(4)'where k is a scalar constant abed s: is the unbiased sample variance, to estimate 1/m forany distribution with the third moment. They proved that ti is an asymptotically unbiasedestimator with bias of or…     

ON THE THEORY OF RESOLVENTS AND ITS APPLICATIONS

1.IntroductionSomefrequentlyusedalgebraicalgorithmssharethesamepropertythattheytransformasetofpolynomialequationstoasinglepolynomialequationsuchthatthezerosetofthepolynomialsetandthehypersurfacedefinedbythesinglepolynomialareequivalentincertainsense.FOralgorithmswiththisproperty,wemaymention'thealgorithmtofindaprimitiveelementforafinitelygeneratedalgebraicextensionfield[1],thealgorithmtofindaplanecurvewhichisbirationaltoaspacealgebraiccur.e[2]!etc.Inthispaper,wepresentageneralalgorithmwhichcan…     

A GENERALIZATION OF ROUTH-HURWITZ CRITERION

1.IntroductionInmanyapplications,oneneedstoknoworestimatetherootsofapolynomialwithrealcoefficients.Thewell--knownRouth--Hurwitzcriterionisanefficienttool,butitappliesonlytotherobustcases;ifsomeofthedeterminantsarezerotitfailstotelliftheseeigenvaluesstillhavenegativerealpartsornot.ThispapergeneralizestheRouth-Hurwitzcriteriontothecriticalcases,wheresomeoftheeigenvaluesofthepolynomiallieontheimaginaryaxis,thispolynomailiscalledasemistablepolynomial.Thetheoremspresentedinthispapergiveanefficien…     

BEHAVIOR OF STOCHASTIC APPROXIMATION ALGORITHM IN ROOT SET OF REGRESSION FUNCTION

1.IntroductionStochasticapproximation(SA)iswidelyappliedinoptimization,systemindelltification,adaptivecontrolandsignalprocessing.ThebasicproblemofSAistoseektherootsoreXtremaofafunctionf(.)calledregressionfunctionwhichcanbeestimateattimekandletthe(k 1)thobservationi,e,Yk 1~f(Xk) ek 1,(1)whereek 1istheobservationnoise.RobbinsandMonroll]in1951proposedthefollowingalgorithmxk l=xk akyk 1,(2)toestimatetherootsofj(.),whereahisthestepsize.ThisalgorithmisnowcalledRobbinsMonro(RM)algorithm.Denoteb…     

ON THE CONVERGENCE ANALYSIS OF ALGORITHMS FOR GENERALIZED SET-VALUEDVARIATIONAL INCLUSIONS IN BANACH SPACES

In this paper, we are devoted to the convergence analysis of algorithms forgeneralized set-valued variational inclusions in Banach spaces. Our results improve, extend,and develop the earlier and recent corresponding results.     

ON THE INVARIANT FOR A FAMILY OF DEFORMED HALLEY METHODS

In this paper,an invariant determined by a function used to guarantee the convergence of all members with ι≤κ in the family of deformed Halley iterative methods for solving nonlinear equation in complex field is given.Results include some known ones as this special cases.We get not only the error estimates of the iterative sequences ｛zn,ι｝ but also those of f(zn,ι) for all ι≤κ.     

SOME DISCUSSION ON THE CONDITIONS OF COMPLETE CONVERGENCE FOR SUMS OF B-VALUED RANDOM ELEMENTSS

1. Introduction and Main ResultsSince the definition on complete convergence of real random variables was introduced by Hsuand Robbins[1], there have been extensive literature on the complete convergence of i.i.d. realvalued random variables, see Baum and Katz ([2]), Bat and Su ([3]). In 1989, Yul4] extendedsome results in Bat and Su ([3]) to real valued independent but not necessarily identicallydistributed case. The main purpose of this paper is to extend the results of Yu[4] to B-value…